Method and Apparatus for Determining Cardiac Performance in a Patient

ABSTRACT

An apparatus for determining heart transplant rejection of a heart in a patient includes at least two electrodes adapted to be sewn into the heart that span the left ventricle. The apparatus includes a voltage generator adapted to be inserted in the patient which generates a voltage to the two electrodes and senses the resulting voltage from the two electrodes. A method for determining heart transplant rejection of a heart in a patient. A pacemaker for a patient (including bi-ventricular pacing and AICDs). The pacemaker includes an RV lead having four electrodes adapted to be inserted into the RV apex. The pacemaker includes a voltage generator which generates a voltage signal to the electrodes and senses the instantaneous voltage along the length of the RV and determines the real and imaginary components to remove the myocardial components of the septum and RV free wall to determine absolute RV blood volume. The pacemaker includes a battery connected to the voltage generator. The pacemaker includes a defibrillator connected to the battery. The pacemaker can also be a bi-ventricular pacemaker to restore RV and LV synchrony during contraction. A method for assisting a heart of a patient.

CROSS-REFERENCE TO RELATED APPLICATIONS

This is a continuation of U.S. patent application Ser. No. 12/086,040 filed Jun. 4, 2008, which is a 371 of international application PCT/U.S. Ser. No. 06/047,649 filed Dec. 14, 2006 and claims the benefit of U.S. provisional application Ser. No. 60/753,105 filed Dec. 22, 2005, and is a continuation-in-part of U.S. patent application Ser. No. 13/066,201 filed Apr. 8, 2011, which is a divisional of U.S. patent application Ser. No. 10/568,912 filed Nov. 1, 2007, now U.S. Pat. No. 7,925,335 issued Apr. 12, 2011, which is a 371 of international application PCT/US04/28573 filed Sep. 3, 2004 and claims the benefit of U.S. provisional application Ser. No. 60/501,749 filed Sep. 9, 2003, all of which are incorporated by reference herein.

FIELD OF THE INVENTION

The present invention is related to measuring instantaneous ventricular volume in the heart of a patient. More specifically, the present invention is related to measuring instantaneous ventricular volume in the heart of a patient by removing the contributor to conductance of muscle, and applying a non-linear relationship to the measured conductance and the volume of blood in the heart including a failing dilated heart (either right or left ventricle) with reduced function and may have an Automatic Implantable Cardiac Defibrillator (AICD) and/or pacemaker. The present invention also allows determination of heart transplant rejection by telemetry to avoid the use of myocardial biopsy.

BACKGROUND OF THE INVENTION

Measurements of electrical conductance using a tetrapolar admittance catheter are used to estimate instantaneous ventricular volume in animals and humans. The measurements of volume are plotted against ventricular pressure to determine several important parameters of cardiac physiologic function. A significant source of uncertainty in the measurement is parallel conductance due to current in the ventricular muscle. The estimated volume is larger than the blood volume alone, which is required for the diagnostic measurement. Furthermore, presently, a linear relationship between conductance and estimated volume is used to calibrate the measurements. The actual relationship is substantially nonlinear.

The invention comprises an improved method for estimating instantaneous blood volume in a ventricle by subtracting the muscle contribution form the total conductance measured. The method relies on measuring the complex admittance, rather than apparent conductance (admittance magnitude), as is presently done. Briefly, the improvement consists of measuring the phase angle in addition to admittance magnitude and then directly subtracting the muscle component from the combined measurement, thereby improving the estimate of instantaneous blood volume. The technique works because the electrical properties of muscle are frequency-dependent, while those of blood are not. This calibration technique is a substantial improvement in clinical and research instrumentation calibration methods.

The invention comprises an improved method for estimating instantaneous volume of a ventricle by applying a nonlinear relationship between the measured conductance and the volume of blood in the surrounding space. The nonlinear calibration relation has been determined from experiments and numerical model studies. This calibration technique is a substantial improvement in clinical and research instrumentation calibration methods.

SUMMARY OF THE INVENTION

The present invention pertains to an apparatus for determining cardiac performance or volume in the patient. The apparatus comprises a conductance (admittance) catheter for measuring conductance and blood volume in a heart chamber of the patient. The apparatus comprises a processor for determining instantaneous volume of the ventricle by applying a non-linear relationship between the measured conductance and the volume of blood in the heart chamber to identify mechanical strength of the chamber. The processor is in communication with the conductance (admittance) catheter.

The present invention pertains to a method for determining cardiac performance in the patient. The method comprises the steps of measuring conductance and blood volume in a heart chamber of the patient with a conductance catheter. There is the step of determining instantaneous volume of the ventricle by applying a non-linear relationship between the measured conductance and the volume of blood in the heart chamber to identify mechanical strength of the chamber with a processor as well as the volume of that chamber. The processor in communication with the conductance (admittance) catheter.

The present invention pertains to an apparatus for determining cardiac performance in a patient. The apparatus comprises a conductance (admittance) catheter for measuring conductance in a heart chamber of the patient, where the conductance includes contributions from blood and muscle with respect to the heart chamber. The apparatus comprises a processor for determining instantaneous volume of the heart chamber by removing the muscle contribution from the conductance. The processor is in communication with the conductance (admittance) catheter.

The present invention pertains to a method for determining cardiac performance in a patient. The method comprises the steps of measuring conductance in a heart chamber of the patient with a conductance (admittance) catheter, where the conductance includes contributions from blood and muscle with respect to the heart chamber. There is the step of determining instantaneous volume of the heart chamber by removing the muscle contribution from the conductance with a processor, the processor in communication with the conductance catheter.

The present invention pertains to an apparatus for determining cardiac performance in the patient. The apparatus comprises a conductance (admittance) catheter having measuring electrodes for measuring conductance in a heart chamber of the patient. The apparatus comprises a processor for determining instantaneous volume of the heart chamber according to

${{Vol}(t)} = {{\left\lbrack {\beta (G)} \right\rbrack \left\lbrack \frac{L^{2}}{\sigma_{b}} \right\rbrack}\left\lbrack {{Y(t)} - Y_{p}} \right\rbrack}$

where: β(G)=the field geometry calibration function (dimensionless), Y(t)=the measured combined admittance, σ_(b) is blood conductivity, L is distance between measuring electrodes, and Y_(p)=the parallel leakage admittance, dominated by cardiac muscle, the processor in communication with the conductance catheter.

The present invention pertains to a method for determining cardiac performance in the patient. The method comprises the steps of measuring conductance and blood volume in a heart chamber of the patient with a conductance (admittance) catheter having measuring electrodes. There is the step of determining instantaneous volume of the ventricle according to

${{Vol}(t)} = {{\left\lbrack {\beta (G)} \right\rbrack \left\lbrack \frac{L^{2}}{\sigma_{b}} \right\rbrack}\left\lbrack {{Y(t)} - Y_{p}} \right\rbrack}$

where: β(G)=the field geometry calibration function (dimensionless), Y(t)=the measured combined admittance, σ_(b) is blood conductivity, L is distance between measuring electrodes, and Y_(p)=the parallel leakage admittance, dominated by cardiac muscle, to identify mechanical strength of the chamber with a processor. The processor is in communication with the conductance (admittance) catheter.

The present invention pertains to an apparatus for determining heart transplant rejection of a heart in a patient. The apparatus comprises at least two electrodes adapted to be sewn into the heart that span the left ventricle. The apparatus comprises a voltage generator adapted to be inserted in the patient which generates a voltage to the two electrodes and senses the resulting voltage from the myocardium to determine if the electrical properties of the myocardium have changed due to rejection, in place of the current standard of myocardial biopsy.

The present invention pertains to a method for determining heart transplant rejection of a heart in a patient. The method comprises the steps of sewing into the heart at least two electrodes that span the left ventricle. There is the step of inserting in the patient a voltage generator which generates a voltage to the two electrodes and senses the resulting voltage from the myocardium.

The present invention pertains to a pacemaker for a patient. The type of pacemaker can include a bi-ventricular pacemaker for resynchronization therapy. The pacemaker comprises in part an RV lead having four electrodes which span the RV chamber and are adapted to be inserted into the RV apex with at least one of the four electrodes placed in either the right atrium or veins drawing into the right heart of the patient. The pacemaker comprises a voltage generator which generates a voltage signal to the electrodes and senses the instantaneous voltage in the RV and determines the real and imaginary components to remove the myocardial component from the septum and RV free wall to determine absolute RV blood volume. The pacemaker comprises a battery connected to the voltage generator. The pacemaker comprises a defibrillator connected to the battery, and/or a bi-ventricular pacemaker for resynchronization therapy.

The present invention pertains to a method for assisting a heart of a patient. The method comprises the steps of inserting into the RV apex an RV lead of a pacemaker/bi-ventricular pacemaker and/or AICD having four electrodes that span the length of the RV. There is the step of generating a voltage signal to the electrodes from a voltage generator. There is the step of sensing the instantaneous voltage in the RV with the voltage generator to determine the real and imaginary components of the voltage to remove the myocardial component from the septum and RV free wall to determine absolute RV blood volume, or rather than remove it, focus on the signal from the septum and RV free wall to determine if myocardial rejecting is occurring as in the case of a transplanted heart.

BRIEF DESCRIPTION OF THE DRAWINGS

In the accompanying drawings, the preferred embodiment of the invention and preferred methods of practicing the invention are illustrated in which:

FIG. 1 shows a four electrode catheter in volume cuvette.

FIG. 2 is a plot for estimating parallel conductance.

FIG. 3 is a plot of apparent conductivity of cardiac muscle as a function of frequency in CD1 mice in vivo at 37° C.

FIG. 4 shows a circuit diagram of a catheter and a measurement system for an open circuit load. The small triangles are the common node for the instrument power supply.

FIG. 5 is a plot of catheter phase effects for saline solutions from 720 to 10,000 μS/cm from 1 kHz to 1 MHz. Apparent conductivity (|η|) of saline solutions (μS/cm).

FIG. 6 is a plot of conductance vs. volume in mouse-sized calibration cuvette.

FIG. 7 is a schematic representation of the apparatus of the present invention.

FIG. 8 is a cylinder-shaped murine LV model: both blood and myocardium are modeled as cylinders.

FIG. 9 is a comparison between true volume and estimated volume by the new and Baan's equations in FEMLAB simulations.

FIG. 10 is a comparison between true volume and estimated volume using the new and Baan's equations in saline experiments.

FIG. 11 is a representation of an apparatus for determining heart transplant rejection of a heart in a patient of the present invention.

FIG. 12 is a representation of a penetrating transducer of the present invention.

FIG. 13 is a representation of a bottom view of a surface transducer of the present invention.

FIG. 14 is a representation of a side view of the surface transducer.

FIG. 15 is a representation of the various embodiments of the present invention as applied to the heart.

FIG. 16 is a representation of a first embodiment regarding possible placement of the apparatus for determining heart transplant rejection.

FIG. 17 is a representation of an alternative placement of electronic instrumentation regarding the apparatus for determining heart transplant rejection.

FIG. 18 is a representation of a pacemaker for a patient according to the present invention.

FIG. 19 shows a tetrapolar RV measurement using dual chamber RV ICD lead.

DETAILED DESCRIPTION

Referring now to the drawings wherein like reference numerals refer to similar or identical parts throughout the several views, and more specifically to FIG. 7 thereof, there is shown an apparatus for determining cardiac performance in the patient. The apparatus comprises a conductance (admittance) catheter 12 for measuring conductance and blood volume in a heart chamber of the patient. The apparatus comprises a processor 14 for determining instantaneous volume of the ventricle by applying a non-linear relationship between the measured conductance and the volume of blood in the heart chamber to identify mechanical strength of the chamber. The processor 14 is in communication with the conductance catheter 12.

Preferably, the apparatus includes a pressure sensor 16 for measuring instantaneous pressure of the heart chamber in communication with the processor 14. The processor 14 preferably produces a plurality of desired wave forms at desired frequencies for the conductance (admittance) catheter 12. Preferably, the processor 14 produces the plurality of desired wave forms at desired frequencies simultaneously, and the processor 14 separates the plurality of desired wave forms at desired frequencies the processor 14 receives from the conductance (admittance) catheter 12. The conductance (admittance) catheter 12 preferably includes a plurality of electrodes 18 to measure a least one segmental volume of the heart chamber.

Preferably, the non-linear relationship depends on a number of the electrodes 18, dimensions and spacing of the electrodes 18, and an electrical conductivity of a medium in which the electrodes 18 of the catheter 12 are disposed. The non-linear relationship may be expressed as (or a substantially similar mathematical form):

β(G)(σ=0.928S/m)=1+1.774(10^(7.481×10) ⁻⁴ ^((G−2057)))

Alternatively, an approximate calibration factor may be used with similar accuracy of the form (or its mathematical equivalent):

β≅e ^(γG) ^(b) ²

where: G is the measured conductance (S), the calculations have been corrected to the conductivity of whole blood at body temperature (0.928 S/m), and 2057 is the asymptotic conductance in μS when the cuvette is filled with a large volume of whole blood. Preferably,

${{Vol}(t)} = {{\left\lbrack {\beta (G)} \right\rbrack \left\lbrack \frac{L^{2}}{\sigma_{b}} \right\rbrack}\left\lbrack {{Y(t)} - Y_{p}} \right\rbrack}$

where: β(G)=the field geometry calibration function (dimensionless), Y(t)=the measured combined admittance, σ_(b) is blood conductivity, L is distance between measuring electrodes, and Y_(p)=the parallel leakage admittance, dominated by cardiac muscle.

The pressure sensor 16 preferably is in contact with the conductance (admittance) catheter 12 to measure ventricular pressure in the chamber. Preferably, the plurality of electrodes 18 includes intermediate electrodes 20 to measure the instantaneous voltage signal from the heart, and outer electrodes 22 to which a current is applied from the processor 14. The pressure sensor 16 preferably is disposed between the intermediate electrodes 20. Preferably, the processor 14 includes a computer 24 with a signal synthesizer 26 which produces the plurality of desired wave forms at desired frequencies and a data acquisition mechanism 28 for receiving and separating the plurality of desired wave forms at desired frequencies. The computer 24 preferably converts conductance into a volume. Preferably, the computer 24 produces a drive signal having a plurality of desired wave forms at desired frequencies to drive the conductance (admittance) catheter 12.

The present invention pertains to a method for determining cardiac performance in the patient. The method comprises the steps of measuring conductance and blood volume in a heart chamber of the patient with a conductance (admittance) catheter 12. There is the step of determining instantaneous volume of the ventricle by applying a non-linear relationship between the measured conductance and the volume of blood in the heart chamber to identify mechanical strength of the chamber with a processor 14. The processor 14 in communication with the conductance (admittance) catheter 12.

Preferably, there is the step of measuring instantaneous pressure of the heart chamber with a pressure sensor 16 in communication with the processor 14. There is preferably the step of producing a plurality of desired wave forms at desired frequencies for the conductance (admittance) catheter 12. Preferably, the producing step includes the step of producing the plurality of desired wave forms at desired frequencies simultaneously, and including the step of the processor 14 separating the plurality of desired wave forms at desired frequencies the processor 14 received from the conductance catheter 12. The producing step preferably includes the step of producing with the processor 14 the plurality of desired wave forms at desired frequencies simultaneously.

Preferably, the determining step includes the step of applying the non-linear relationship according to the following (or its mathematical equivalent):

β(G)(σ=0.928S/m)=1+1.774(10^(7.481×10) ⁻⁴ ^((G−2057)))

where: G is the measured conductance (S), the calculations have been corrected to the conductivity of whole blood at body temperature (0.928 S/m), and 2057 is the asymptotic conductance in μS when the cuvette is filled with a large volume of whole blood. Or, alternatively, an approximate geometry calibration factor may be used:

β=e ^(γ[G) ^(b) ^(]) ²

where α is determined experimentally or from mathematical calculations or numerical models.

The determining step preferably includes the step of determining instantaneous volume according to

${{Vol}(t)} = {{\left\lbrack {\beta (G)} \right\rbrack \left\lbrack \frac{L^{2}}{\sigma_{b}} \right\rbrack}\left\lbrack {{Y(t)} - Y_{p}} \right\rbrack}$

where: β(G)=the field geometry calibration function (dimensionless), Y(t)=the measured combined admittance, σ_(b) is blood conductivity, L is distance between measuring electrodes, and Y_(p)=the parallel leakage admittance, dominated by cardiac muscle.

Preferably, the step of measuring instantaneous pressure includes the step of measuring instantaneous pressure with the pressure sensor 16 in contact with the conductance (admittance) catheter 12 to measure the ventricular pressure in the chamber. The measuring step preferably includes the step of measuring at least one segmental volume of the heart chamber with a plurality of electrodes 18 on the conductance (admittance) catheter 12. Preferably, the measuring step includes the steps of applying a current to outer electrodes 22 of the plurality of electrodes 18 from the processor 14, and measuring an instantaneous voltage signal from the heart with intermediate electrodes 20 of the plurality of electrodes 18.

The step of measuring instantaneous pressure preferably includes the step of measuring instantaneous pressure with the pressure sensor 16 disposed between the intermediate electrodes 20 and the outer electrodes 22. Preferably, the producing with the processor 14 step includes the step of producing with a signal synthesizer 26 of a computer 24 the plurality of desired wave forms at desired frequencies, and the processor 14 separating step includes the step of receiving and separating the plurality of desired wave forms at desired frequencies with a data acquisition mechanism 28 of the computer 24. There is preferably the step of converting conductance into a volume with the computer 24. Preferably, there is the step of producing with the computer 24 a drive signal having the plurality of desired wave forms at desired frequencies to drive the conductance (admittance) catheter 12.

The present invention pertains to an apparatus for determining cardiac performance in a patient. The apparatus comprises a conductance (admittance) catheter 12 for measuring conductance in a heart chamber of the patient, where the conductance includes contributions from blood and muscle with respect to the heart chamber. The apparatus comprises a processor 14 for determining instantaneous volume of the heart chamber by removing the muscle contribution from the conductance. The processor 14 is in communication with the conductance catheter 12.

Preferably, the apparatus includes a pressure sensor 16 for measuring instantaneous pressure of the heart chamber in communication with the processor 14. The processor 14 preferably produces a plurality of desired wave forms at desired frequencies for the conductance (admittance) catheter 12. Preferably, the processor 14 produces the plurality of desired wave forms at desired frequencies simultaneously, and the processor 14 separates the plurality of desired wave forms at desired frequencies the processor 14 receives from the conductance (admittance) catheter 12. The processor 14 preferably measures complex admittance with the conductance (admittance) catheter 12 to identify the muscle contribution.

Preferably, the complex admittance is defined as

Y _(p) =Gm+jωCm(Y subscript p)

where

-   -   Cm=capacitance component of muscle (F=Farads) (C subscript m)     -   ω=angular frequency (radians/second) (greek “omega”=2 pi f)

Gm=conductance of muscle (S=Siemens) (G subscript m). The conductance preferably is defined as

Y(t)=Gb+Gm+jωCm

where Gb=conductance of blood (S) (G subscript b).

The present invention pertains to a method for determining cardiac performance in a patient. The method comprises the steps of measuring conductance in a heart chamber of the patient with a conductance (admittance) catheter 12, where the conductance includes contributions from blood and muscle with respect to the heart chamber. There is the step of determining instantaneous volume of the heart chamber by removing the muscle contribution from the conductance with a processor 14, the processor 14 in communication with the conductance (admittance) catheter 12.

Preferably, there is the step of measuring instantaneous pressure of the heart chamber with a pressure sensor 16 in communication with the processor 14. There is preferably the step of producing a plurality of desired wave forms at desired frequencies for the conductance (admittance) catheter 12. Preferably, the producing step includes the step of producing the plurality of desired wave forms at desired frequencies simultaneously, and including the step of the processor 14 separating the plurality of desired wave forms at desired frequencies the processor 14 received from the conductance catheter 12. The producing step preferably includes the step of producing with the processor 14 the plurality of desired wave forms at desired frequencies simultaneously. Preferably, there is the step of measuring complex admittance with the conductance catheter 12 to identify the muscle contribution.

The measuring the complex admittance step preferably includes the step of measuring the complex admittance according to

Yp=Gm+jωCm(Y subscript p)

where

-   -   Cm=capacitance component of muscle (F=Farads) (C subscript m)     -   ω=angular frequency (radians/second) (greek “omega”=2 pi f)     -   Gm=conductance of muscle (S=Siemens) (G subscript m).

Preferably, the determining step includes the step of determining instantaneous volume based on conductance defined as

Y(t)=Gb+Gm+jωCm

where Gb=conductance of blood (5) (G subscript b).

The present invention pertains to an apparatus for determining cardiac performance in the patient. The apparatus comprises a conductance (admittance) catheter 12 for measuring conductance in a heart chamber of the patient. The apparatus comprises a processor 14 for determining instantaneous volume of the heart chamber according to

${{Vol}(t)} = {{\left\lbrack {\beta (G)} \right\rbrack \left\lbrack \frac{L^{2}}{\sigma_{b}} \right\rbrack}\left\lbrack {{Y(t)} - Y_{p}} \right\rbrack}$

where: β(G)=the field geometry calibration function (dimensionless), Y(t)=the measured combined admittance, σ_(b) is blood conductivity, L is distance between measuring electrodes, and Y_(p)=the parallel leakage admittance, dominated by cardiac muscle, the processor 14 in communication with the conductance catheter 12.

The present invention pertains to a method for determining cardiac performance in the patient. The method comprises the steps of measuring conductance and blood volume in a heart chamber of the patient with a conductance (admittance) catheter 12. There is the step of determining instantaneous volume of the ventricle according to

${{Vol}(t)} = {{\left\lbrack {\beta (G)} \right\rbrack \left\lbrack \frac{L^{2}}{\sigma_{b}} \right\rbrack}\left\lbrack {{Y(t)} - Y_{p}} \right\rbrack}$

where: β(G)=the field geometry calibration function (dimensionless), Y(t)=the measured combined admittance, σ_(b) is blood conductivity, L is distance between measuring electrodes, and Y_(p)=the parallel leakage admittance, dominated by cardiac muscle, to identify mechanical strength of the chamber with a processor 14. The processor 14 is in communication with the conductance catheter 12.

The classic means to determine left ventricular pressure-volume (PV) relationships in patients on a beat-by-beat basis is through the use of the conductance (volume/admittance) catheter 12. The electric field that it creates in the human left or right ventricle at the time of heart catheterization is the only technology capable of measuring instantaneous left and/or right ventricular volume during maneuvers such as transient occlusion of the inferior vena cava. Such maneuvers allow determination of the wealth of information available from the PV plane including: end-systolic elastance, diastolic compliance, and effective arterial elastance. However, use of conductance technology in patients with dilated hearts whose LV volumes can range from 200 to 500 ml has been problematic.

The G-V method measures the conductance between electrodes 18 located in the LV and aorta. A minimum of four electrodes 18 is required to prevent the series impedance of the electrode-electrolyte interfaces from distorting the measurement. Typically, the two current source-sink electrodes are located in the aorta and in the LV near the apex (electrodes 1 and 4 in FIG. 1).

The potential difference between the potential measuring electrodes (2 and 3) is used to calculate the conductance: G=I/V. The governing assumption is that the current density field is sufficiently uniform that the volume and conductance are simply related by Baan's equation [1]:

$\begin{matrix} {{{Vol}(t)} = {{\left\lbrack \frac{1}{\alpha} \right\rbrack \left\lbrack \frac{L^{2}}{\sigma_{b}} \right\rbrack}\left\lbrack {{G(t)} - G_{p}} \right\rbrack}} & (1) \end{matrix}$

where: α is the geometry factor (a dimensionless constant), L is the center-to-center distance between voltage sensing electrodes (2 and 3) (m), σ_(b) is the conductivity of blood (S/m), G(t) is the measured instantaneous conductance (S), and G_(p) is the parallel conductance (S) in cardiac muscle (G_(p)=0 in the calibration cuvette of FIG. 1).

Two limitations inherent in the state-of-the-art technique interfere with accurate measurements: 1) the electric field around the sensing electrodes 18 is not uniform, leading to a non-linear relationship between measured conductance and ventricular volume which has decidedly lower sensitivity to large volumes, and 2) the parallel conductance signal added by surrounding cardiac muscle adds virtual volume to the measurement. The new technique improves the estimate of the parallel muscle conductance based on the measurement of complex admittance at two or more frequencies, rather than using the admittance magnitude, as is presently done. Furthermore, the inherent non-linearity of conductance vs. volume is usually compensated by establishing apiece-wise linear approximation to the sensitivity curve (Vol vs. G) in the region of operation. That is, a is actually a function of the diameter of the volume in FIG. 1; but is assumed constant over the operating range of a measurement, ESV to EDV.

The electrical properties of cardiac muscle are frequency-dependent [6-14] while those of blood are not [15-18]. The admittance measurement at (at least) one frequency can be used to separate the muscle component from the combined muscle-blood signal. Measurement of the phase angle of the admittance is a more sensitive indicator of the muscle signal than the magnitude of the admittance, which is currently measured. Information contained in the phase angle can improve the overall accuracy of the single and/or dual frequency admittance system. This reformulation of the measurement allows one to verify that the effective sensing volume actually reaches the ventricular muscle in the case of an enlarged heart.

In the operation of the invention, the parallel conductance signal is presently compensated by three methods: 1) hypertonic saline injection [19, 20], 2) occlusion of the inferior vena cava (IVC) [21], and 3) conductance measurement at one or two frequencies [22, 23]. In the first approach, a known volume of hypertonic saline (usually 10% NaCl) is injected and the beat-by-beat conductance signal measured as it washes through the LV during several beats. The End Diastolic Conductance (EDG) is plotted against End Systolic Conductance (ESG), and the resulting line is projected back to the line of equal values (EDG=ESG when stroke volume=0), and the remainder is the estimate of parallel conductance, G_(p). (see FIG. 2.). In the second approach, occlusion of the IVC, shrinks the LV volume, but the result is analyzed in the same way as FIG. 2. The third approach attempted to use the frequency dependence of muscle to identify the parallel conductance [22, 23]. This is similar to the approach described here, but different in that the particular frequencies were limited to a maximum of about 30 kHz and only the magnitude of the combined signal was used. A maximum frequency of 100 kHz is used here to better separate the muscle from the combined signal; further, the phase angle is a much more sensitive indicator of muscle than admittance magnitude alone. Also, the use of the phase angle and magnitude of the admittance signal allows as few as a single frequency to be utilized in an accurate fashion, not possible with a single frequency magnitude device.

Each of the parallel conductance compensation approaches has undesirable features. Hypertonic saline injection creates an a physiologic electrolyte load that is undesirable in the failing heart. IVC occlusion brings the ventricular free wall and septum closer to the electrode array and artificially elevates the parallel conductance. The dual frequency magnitude only measurements are able to identify a difference signal between blood and cardiac muscle, but measurement using the magnitude of admittance alone is not sufficiently sensitive to yield satisfying results, and the particular frequencies used in the past are not the best to separate the two signals. Further, the use of phase angle and magnitude of the admittance signal alone can be performed accurately using a single frequency. There are other considerations in the dual-frequency magnitude only measurement which affect overall accuracy—notably the parasitic impedances in the catheter 12 itself—which must be compensated before reliable calculations may be made. The present invention is a significant improvement to the dual frequency magnitude only method; it uses measurements of the complex admittance to more accurately identify the parallel muscle volume signal and does not require injecting fluids or changing the LV volume to complete.

Frequency Dependence of Muscle Electrical Properties:

Electrolytic solutions, blood and all semiconducting materials have an electrical conductivity, a, that is essentially independent of frequency. Dielectric materials have an electric permittivity, ∈ (F/m): in essence, permittivity is a measure of the polarizable dipole moment per unit volume in a material [14]. A general material has both semiconducting and dielectric properties, and each aspect contributes to the total current density vector, J_(tot)(A/m²) in a vector electric field, E (V/m). The conductivity, σ, results in conduction current density according to Ohm's Law, and the permittivity, ∈, contributes “displacement” current density in a harmonic (i.e. sinusoidal) electric field, as reflected in the right hand side of Ampere's Law [40]:

J _(tot)=(σ+jω∈)E  (2)

where: j=√{square root over (−1)} and ω=2πf=the angular frequency (r/s). J_(tot) is complex even if E is real—in other words, J and E are not in phase with each other unless ω∈ is small with respect to σ. Most all tissues behave as semiconductors at all frequencies below about 10 MHz because σ>>ω∈. The remarkable exception is muscle tissue in vivo or very freshly excised, [10-12, and our own unpublished measurements]. To calibrate this discussion, water has a very strong dipole moment, and has a relative permittivity of around 80 at frequencies below about 1 MHz; and the relative permittivities of most tissues are, therefore, usually dominated by their water content. Muscle, in contrast, has a very high relative permittivity: around 16,000 in the 10 kHz to 100 kHz range (almost 200 times that of water) [11], owing to the trans-membrane charge distribution. Consequently, cue are able to observe the frequency dependence of muscle total current density since we is larger than a for frequencies above about 15 kHz.

For example, the apparent conductivity of murine cardiac muscle using a surface tetrapolar probe shows a reliable and repeatable frequency dependence. In FIG. 3, the indicated conductivity increases significantly above about 10 kHz. The conductivity in the figure includes some permittivity effects: the measurement device actually indicates the magnitude of the (σ+jω∈) term in equation 2. For muscle, it is more accurate to think in terms of “admittivity”, η=σ+jω∈. σ=1,800 μS/cm (0.18 S/m) from the low frequency portion of the plot, and estimate that ∈=16,000 ∈₀ (F/m) which compares well with published data. In the figure, the parasitic capacitances of the surface probe have been compensated out using measurements of the surface probe on electrolytic solutions with the same baseline conductivity as muscle.

Numerical Model Studies:

Numerical models of the murine catheter in a mouse LV were executed at volumes representative of the normal ESV and EDV in the mouse. The numerical model was an enhanced version of the model used for the cuvette studies: each control volume (CV) could be assigned a different value of electrical conductivity, σ. The model spatial resolution and FDM calculational approach were the same as described above. A larger number of iterations were required for convergence, however, around 400,000 iterations. This is because the electrical boundary conditions of the inhomogeneous media substantially increase the number of trials required to settle to the final solution. Models were completed using realistic volumes for ESV and EDV derived from conductance catheter 12 data: 19 μl and 45 μl, respectively (ejection fraction=60%). Electrical conductivities for blood, cardiac muscle and aorta were: σ_(b)=0.928 S/m, σ_(m)=0.0945 S/m at 10 kHz and 0.128 S/m at 100 kHz, σ_(a)=0.52 S/m [41], respectively. All of the properties are real-valued in the model—the complex nature of muscle has not been included in the preliminary studies. The ventricular free wall endocardial surface was treated as a smooth ellipse, and the LV was modeled as an ellipsoid of revolution. The geometry was considerably simplified over the actual LV for two reasons: 1) the purpose of the model was to identify the expected order-of-magnitude of muscle contribution to the measured conductance, 2) the resources and time available did not permit development of a detailed 3-D geometry, nor the use of more accurate finite element method (FEM) models.

Table 1 compares FDM model and experiment data. The model consistently under-estimates the measured conductances: by about 11% and 35% at 10 kHz, and by 30% and 47% at 100 kHz. The comparisons at 10 kHz are least sensitive to uncertainty in tissue electrical properties and catheter 12 effects. Deviations at this frequency are more likely due to geometric simplifications in the model and under-estimation of the appropriate LV volume to use.

TABLE 1 Summary of model and experimental conductance values (μS). Experimental data are the means of six normal mice [28], numbers in parentheses are standard deviations. Source EDV ESV FDM Model @ 10 kHz 1419 μS 844 μS Experiment @ 10 kHz 1600 (500) 1300 (400) FDM Model @ 100 kHz 1493 905 Experiment @ 100 kHz 2100 (400) 1700 (400)

The 100 kHz measurements reveal an additional effect due to the complex nature of the electrical properties of muscle and the effect of capacitance between the wires in the conductance (admittance) catheter 12. While the actual values of the calculated conductance are subject to many uncertainties, the differences between 10 kHz and 100 kHz values in the model are due only to the electrical properties of muscle. So, in Table 1 it looks at first glance as though the model work has severely underestimated the capacitive effects in muscle. However, it must be noted that the reported in vivo measurements do not compensate out the stray capacitance in the catheter 12 at 100 kHz. At this point, it is not clear precisely how much of the apparent frequency-dependent signal is due to catheter 12 capacitance, and how much is due to muscle signal in those data.

The improved muscle parallel conductance compensation technique described can be implemented in existing conductance machines either in embedded analysis software (real-time or off-line processing of measured data) or in dedicated Digital Signal Processing hardware devices.

Phase Angle Measurement:

There is an embedded difficulty in this measurement which must be addressed: the parasitic capacitance of the catheters has effects on the measured admittance signal phase angle in addition to the muscle permittivity component. One necessarily measures the two together; and a method for compensating out or otherwise dealing with the catheter-induced effects is required. Fortunately, all of the necessary catheter 12 characteristics can be measured a priori. We have identified three approaches to this problem.

First, the catheter 12 phase angle effects stem from parasitic capacitance between electrode wires in the catheter 12. The tetrapolar case is relatively easy to discuss, and the multi-electrode catheters consist of several repeated combinations of the 4-electrode subunit. We can measure the six inter-electrode parasitic capacitances of the 4-electrode systems (FIG. 4). The effect of the inter-electrode capacitances can be reduced to a single capacitive admittance in parallel with the tissues, C_(cath), much larger than any of the C_(ij). This can be seen in experimental measurements on saline which has no observable permittivity effects at frequencies below about 200 MHz; thus, all capacitance information (frequency-dependent increase in |η|, where η=σ+jω∈) in the signal comes from catheter 12 effects (FIG. 5). In FIG. 5 a small conductivity measurement probe (inter-electrode capacitances from 60 to 70 pF) has been used to measure the apparent conductivity (|η|) of saline solutions between 720 μS/cm (lowest line) and 10,000 μS/cm (highest line). The lines cross because the point where σ_(NaCl)=ω∈_(cath) moves to higher frequency for higher σ. C_(cath) is approximately 1.5 nF here.

Second, a lumped-parameter circuit model can be constructed for catheter 12 effects and use this model to correct the measured potential, ΔV, to the value it would have in the absence of the parasitic capacitances. Third, we can advance the measurement plane from the current-source output, I_(s), (FIG. 5) and voltage measurement location, ΔV, to the outside surfaces of the four electrodes 18 using a bilinear transform. This is a standard approach in impedance measurement [see ref. 14, Ch. 5] and requires only a measurement at open circuit, short circuit and a normalizing load (say, 1 kΩ) to accomplish.

The first approach is the most practical for implementation in a clinical instrument: we will subtract the catheter 12 capacitance, C_(cath), (measured a priori) from the total capacitance of the measurement, C_(tot), with the remainder: C_(muscle)=C_(tot)−C_(cath). The measurement from 2 to 10 kHz includes only the real parts: Y₁₀=G_(b) G_(musc). At 100 kHz: Y₁₀₀=G_(b) G_(musc)+jω(C_(cath)+C_(musc)). Negative values are rejected and C_(cath) is deterministic and not time-varying. The calculation strategy is then: C_(tot)=|Y₁₀₀|sin(θ_(tot))/ω; C_(musc)=C_(tot)−C_(cath); finally, G_(p)=G_(musc)=σ_(m)C_(musc)/∈_(musc) (from the well known conductance-capacitance analogy [40]) and G_(p) can be subtracted from |Y₁₀| to determine G_(b)—i.e. |Y₁₀|=G_(b)+G_(p). A purely analog approach to this measurement is impossible, and a mixed signal approach with extensive digital processing required for both catheter 12 compensation and phase measurement is used. Based on the model trends and measured values of Table 1, it is estimated the relative phase angles in the measured admittance ought to be approximately 4° for EDV and 8° for ESV. The larger phase angle for ESV reflects the change in relative proximity of the LV wall.

The non uniformity of the electrode sensing field is inherent in the single current source electrode geometry of FIG. 1. Two limiting cases illustrate the origin of this. First, for a sufficiently large cuvette or blood volume, the electric and current density fields surrounding electrodes 1 and 4 are similar in overall shape to those of a current dipole: the magnitude of the current density decreases with the cube of the radius. At very large volume the voltage measured between electrodes 2 and 3 is insensitive to the location of the outer boundary. Consequently, the measured conductance saturates at large volumes since the sensitivity, ΔG/ΔVol=0, and thus α=zero. Second, the other limit is reached when the outer radius of the volume is minimally larger than the catheter 12 itself. In that case the current density approaches a uniform distribution and a approaches 1. Radii between these limits cross over from α=1 to α=0.

The behavior of a was studied in experiments and numerical models of a mouse-sized 4-electrode conductance catheter 12 in a volume-calibration cuvette. This catheter 12 has L=4.5 mm between the centers of electrodes 2 and 3 and is 1.4F (i.e. 0.45 mm in diameter). The cuvette was filled with 1M saline solution (σ=1.52 S/m at room temperature). The results are summarized in FIG. 3. In the Figure, “Ideal G” is the line α=1. The numerically calculated (squares) and measured (circles) conductance in μS are plotted vs. cuvette volume (μl). The measurement sensitivity, ΔG/ΔVol, in the figure=α(σ/L²), and this slope asymptotically approaches 0 for volumes greater than about 150 μl for this catheter 12. This behavior is determined solely by the geometry of the current density field, and α is independent of the conductivity of the solution.

Based on the numerical model and experimental results, a new calibration equation using β(G) as the geometry calibration function to replace a in equation 4:

$\begin{matrix} {{{Vol}(t)} = {{\left\lbrack {\beta (G)} \right\rbrack \left\lbrack \frac{L^{2}}{\sigma_{b}} \right\rbrack}\left\lbrack {{Y(t)} - Y_{p}} \right\rbrack}} & (4) \end{matrix}$

where: β(G)=the field geometry calibration function (dimensionless), Y(t)=the measured combined admittance, σ_(b) is blood conductivity, L is distance between measuring electrodes, and Y_(p)=the parallel “leakage” admittance, dominated by cardiac muscle. At small volumes, β(G)=α=1. At large volumes, β(G) increases without bound, as expected from the model work in FIG. 6. The new calibration function includes the non-linear nature of the volume calculation: since for a particular catheter β(G) depends on the conductivity of the liquid and on measured G—i.e. on cuvette and/or ventricular blood outer radius—it is not simply expressible in terms of 1/α. The expression for β(G) for the mouse-sized catheter 12 described above for FIG. 6 data is:

β(G)(σ=0.928S/m)=1+1.774(10^(7.481×10) ⁻⁴ ^((G−2057)))  (5)

where: G is the measured conductance (S), the calculations have been corrected to the conductivity of whole blood at body temperature (0.928 S/m), and 2057 is the asymptotic conductance in μS when the cuvette is filled with a large volume of whole blood. Here β(G) depends only on the real part of Y because the cuvette measurements do not contain muscle. In use, G is the real part of [Y(t)−Y_(p)], and any imaginary part of the signal is rejected since it must come from a muscle component, or from the instrumentation. As required, β(G) approaches 1 as G becomes small compared to the asymptote, 2057 μS.

The improved calibration method can be implemented in existing conductance machines either in embedded analysis software (real-time or off-line processing of measured data) or in dedicated Digital Signal Processing hardware devices.

Complex admittance in regard to overall admittance as it relates to Y(t)−Y_(p) is as follows.

Y(t)=Gb+Gm+jωCm

Y _(p) =Gm+jωCm(Y _(p))

-   -   C_(m)=capacitance component of muscle (F=Farads) (C_(m))     -   ω=angular frequency (radians/second) (ω=2πf)     -   Gm=conductance of muscle (S=Siemens) (G_(m))     -   Gb=conductance of blood (S) (G_(b))

Y(t)=total instantaneous measured admittance (S) (after catheter 12 effects have been compensated.

Y_(p)=total parallel admittance (everything but blood). The cardiac muscle dominates Y_(p); and thus once Y_(p) is known (from the measurement of phase angle—only muscle has capacitance and contributes to the phase angle) the estimate of G_(b) can be improved and thus the volume of blood.

The following elaborates on the nonlinear relationship β(G) between conductance and volume.

1. Physical Principle:

β(G) is a nonlinear function for every admittance (conductance) catheter 12. The function depends on the number, dimensions and spacing of the electrodes 18 used, and on the electrical conductivity of the medium which it is in. β(G) is determined by the shape of the current field created by the electrodes 18.

2. Experimental Determination

β(G) may be determined experimentally for any conductance catheter 12 in cylindrical “cuvettes” in which a solution of known electrical conductivity is measured over a range of cuvette diameters. The “volume” is the volume of solution between the voltage sensing electrodes 18.

3. Determination by Solution of the Electric Field Equations

β(G) may also be determined by solving the governing electric field equations, namely Gauss' Electric Law—either in integral form or in the form of the Laplace at low frequency, and the wave equations at high frequency—subject to appropriate boundary conditions. The solution may be by analytical means (paper and pencil) or by numerical means, as in a digital computer 24 model of the electric and/or electromagnetic fields. For any current field established by two or more electrodes 18 a model yields the measured conductance when the total current—surface integral of (sigma mag(E) dot product dS), where dS is the elemental area—is divided by the measurement electrode voltage, from the model or calculation results. Many books on electromagnetic field theory teach how to make the calculation. A specific reference is Chapter 6 (p. 184) in W. H. Hayt and J. A. Buck “Engineering Electromagnetics”, 6th Edition McGraw-Hill, Boston, 2001, incorporated by reference herein. The specific reference teaches how to calculate resistance, R, but conductance, G is simply the reciprocal of R, G=1/R. The calculated G may be a complex number (for mixed materials like tissues), in which case the catheter 12 measures “admittance”, Y, a complex number.

(A) Measured Conductance and Capacitance Signals

Two of the catheter electrodes (#1 and #4) are used to establish a current field in the ventricle. The current field results in an electric field in the tissues, the strength of which is determined by measuring the voltage between electrodes #2 and #3. Because electrodes 2 and 3 carry negligible amounts of current, they provide a useful estimate of the electric field in the tissues. The current supplied to the tissue (electrodes 1 and 4) is divided by the voltage measured between electrodes 2 and 3 to determine the admittance of the tissue, Y (S). The admittance consists of two parts, the Conductance, G (S) the real part, and the Susceptance, B (S), the imaginary part: Y=G+jB. In this measurement, both blood and muscle contribute to the real part of the measured signal, G=G_(b)+G_(musc). However, after all catheter-induced effects have been removed, only the muscle can contribute to the imaginary part, B=jω C_(musc).

For any geometry of electric field distribution in a semiconducting medium, the conductance may be calculated from:

$\begin{matrix} {G = {\frac{I}{V} = \frac{\underset{S}{\int\int}\sigma \; {E \cdot {S}}}{- {\int_{a}^{b}{E \cdot {l}}}}}} & (a) \end{matrix}$

where the surface, S, in the numerator is chosen to enclose all of the current from one of the electrodes used to establish the electric field, E, and the integration pathway in the denominator is from the low voltage “sink” electrode at position “a” to the higher voltage “source” electrode at position “b”. Similarly, for any geometry of electric field in a dielectric medium, the capacitance may be calculated from:

$\begin{matrix} {C = {\frac{Q}{V} = \frac{\underset{S}{\int\int}ɛ\; {E \cdot {S}}}{- {\int_{a}^{b}{E \cdot {l}}}}}} & (b) \end{matrix}$

B) Parallel Admittance in the Cardiac Muscle

The measured tissue signal, Y=G_(b)+G_(musc)+jω C_(musc). From the high frequency measurement C_(musc) may be determined from the measured phase angle by: C_(musc)=|Y|sin (θ)/ω after catheter phase effects have been removed. By equations (a) and (b) above, the muscle conductance can be determined from its capacitance by: G_(musc)=σ/∈ C_(musc) since the two equations differ only by their respective electrical properties—i.e. the electric field geometry calculations are identical in a homogeneous medium. In this way, the muscle conductance (independent of frequency, and thus the same in the low frequency and high frequency measurements) may be determined from the muscle capacitance (observable only in the high frequency measurements).

Beyond these very general relations, a person may make catheter electrode configurations of many shapes and sizes and use them in many sorts of conductive solutions. All would have a different β(G) function.

In an alternative embodiment, the LV and/or RV volume signal is only relative to LV or RV blood conductance, but the measured admittance comes from both blood and myocardium. Therefore, it is desired to extract the blood conductance from the measured admittance, which can be done by using the unique capacitive property of myocardium. To achieve it, the first step is to obtain the conductivity and permittivity of myocardium.

Myocardial Conductivity and Permittivity

It is believed that blood is only conductive, while myocardium is both conductive and capacitive. Therefore, the measured frequency-dependent myocardial “admittivity”, Y′_(m)(f), actually is composed of two components:

Y′ _(m)(f)=√{square root over (σ_(m) ²+(2πf∈ _(r)∈₀)²)}  (6)

where σ_(m) is the real myocardial conductivity, f is frequency, ∈_(r) is the relative myocardial permittivity, and ∈₀ is the permittivity of free space. Experimentally, Y′_(m)(f) can be measured at two different frequencies, such as 10 and 100 kHz, and then the value of σ_(m) and myocardial permittivity ∈ can be calculated by:

$\begin{matrix} {\sigma_{m} = \sqrt{\frac{{100 \cdot \left\lbrack {Y_{m}^{\prime}\left( {10k} \right)} \right\rbrack^{2}} - \left\lbrack {Y_{m}^{\prime}\left( {100k} \right)} \right\rbrack^{2}}{99}}} & (7) \\ {{ɛ \equiv {ɛ_{r}ɛ_{0}}} = {\frac{1}{2{\pi \cdot 10^{4}}}\sqrt{\frac{\left. {Y_{m}^{\prime}\left( {100k} \right)} \right\rbrack^{2} - \left\lbrack {Y_{m}^{\prime}\left( {10k} \right)} \right\rbrack^{2}}{99}}}} & (8) \end{matrix}$

Alternatively, Y′_(m)(f) can be measured at a single frequency, such as 30 kHz, and then the value of σ_(m) and myocardial permittivity can be calculated.

Blood Conductance

In the 10 and 100 kHz dual-frequency measurement system, the measured magnitude of admittance, |Y(f)|, is blood conductance (g_(b)) in parallel with myocardial conductance (g_(m)) and capacitance (C_(m)), shown as

|Y(10k)|=√{square root over ((g _(b) +g _(m))²+(2π·10⁴ C _(m))²)}{square root over ((g _(b) +g _(m))²+(2π·10⁴ C _(m))²)}  (9)

|Y(100k)|=√{square root over ((g _(b) +g _(m))²+(2π·10⁵ C _(m))²)}{square root over ((g _(b) +g _(m))²+(2π·10⁵ C _(m))²)}  (10)

Using equations (9) and (10),

$\begin{matrix} {C_{m} = {\frac{1}{2{\pi \cdot 10^{4}}}\sqrt{\frac{{{Y\left( {100k} \right)}}^{2} - {{Y\left( {10k} \right)}}^{2}}{99}}}} & (11) \\ {{g_{b} + g_{m}} = \sqrt{\frac{{100 \cdot {{Y\left( {10k} \right)}}^{2}} - {{Y\left( {100k} \right)}}^{2}}{99}}} & (12) \end{matrix}$

From the well known conductance-capacitance analogy [40],

$\begin{matrix} {g_{m} = {C_{m}\frac{\sigma_{m}}{ɛ}}} & (13) \end{matrix}$

Substitute eq. (13) into eq. (12), blood conductance g_(b) is obtained as

$\begin{matrix} {g_{b} = {\left( \sqrt{\frac{{100 \cdot {{Y\left( {10k} \right)}}^{2}} - {{Y\left( {100k} \right)}}^{2}}{99}} \right) - g_{m}}} & (14) \end{matrix}$

A new conductance-to-volume conversion equation is

Vol(t)=ρ_(b) L ² g _(b)(t)exp[γ·(g _(b)(t))²]  (15)

where Vol(t) is the instantaneous volume, ρ_(b) is the blood resistivity, L is the distance between the sensing electrodes, g_(b)(t) is the instantaneous blood conductance, and γ is an empirical calibration factor, which is determined by the following steps.

-   -   1. A flow probe is used to measure the LV stroke volume (SV),         denoted as SV_(flow).     -   2. Assign an initial positive number to γ, and use equation (15)         to convert blood conductance to volume signal. The resulting         stroke volume is denoted as SVγ.     -   3. If SVγ is smaller than SV_(flow), increase the value of γ.         Otherwise, decrease it.     -   4. Repeat steps 2 and 3 until it satisfies.

SV _(γ) =SV _(flow)  (16)

Since equation (15) is a monotonic increasing function, there is only one possible positive solution for γ.

This empirical factory is used to compensate and calibrate the overall uncertainty and imperfection of the measurement environment, such as inhomogeneous electrical field and off-center catheter position.

Simulation Results

A commercial finite element software, FEMLAB, is used to simulate this problem. A simplified LV model is created by modeling both LV blood and myocardium as cylinders with a four-electrode catheter inserted into the center of cylinders, as shown in FIG. 8. A similar model could be made for the RV as well.

The radius of the inner blood cylinder was changed to explore the relationship between volume and conductance. Assuming stroke volume is the difference between the largest and smallest blood volume, and this difference is used to determine the empirical calibration factors, a and γ, for Baan's and the new equations respectively. The calculated magnitude of admittance, blood conductance, true volume, and estimated volume by Baan's and the new equations are listed in Table II and also plotted in FIG. 9, where the true volume is the volume between the two inner sensing electrodes. The distance between two inner sensing electrodes for a mouse size catheter is 4.5 mm.

TABLE II Comparison of true and estimated volume by two equations Calculated Estimated Estimated magnitude of Blood True volume by Baan's volume by new admittance conductance volume equation equation (μS) (μS) (μL) (μL) (μL) 2491.1 2344.7 62.9 64.5 62.0 2030.2 1853.3 43.7 51.0 43.1 1514.0 1314.3 28.0 36.2 27.5 1337.7 1133.5 23.5 31.2 23.0 1162.4 956.1 19.4 26.3 19.0 992.5 786.4 15.7 21.6 15.3 829.3 626.2 12.4 17.2 12.0 677.3 479.3 9.5 13.2 9.1 538.1 347.9 7.0 9.6 6.6 414.4 234.2 4.9 6.4 4.4

In Vitro Saline Experiments

Several cylinder holes were drilled in a 1.5-inch thick block of Plexiglas. The conductivity of saline used to fill those holes was 1.03 S/m made by dissolving 0.1 M NaCl in 1 liter of water at 23° C. room temperature, which is about the blood conductivity. A conductance catheter with 9 mm distance between electrodes 2 and 3 is used to measure the conductance.

Since plexiglas is an insulating material, the measured conductance comes from saline only, not from the plexiglas wall. Therefore, the measured saline conductance corresponds to the blood conductance in vivo experiments. Again, stroke volume is assumed to be the difference between the largest and smallest blood volume, and then used to determine the empirical calibration factors, α and γ, for Baan's and the new equations, respectively. The measured data at 10 kHz and the estimated volume by Baan's and the new equations are listed in Table III. The true volume listed is the volume between electrodes 2 and 3. The data are plotted in FIG. 10.

TABLE III Comparison of true and estimated volume in the drilled holes Estimated Estimated Diameter of Measured True volume by Baan's volume by new Drilled holes conductance volume equation equation (inch) (μS) (μL) (μL) (μL) 3/16 1723.5 160.3 562.0 160.5 ¼  2675.0 285.0 872.3 310.3 5/16 3376.0 445.3 1100.9 494.5 ⅜  3836.4 641.3 1251.0 684.8 7/16 4171.0 827.9 1360.1 866.7 ½  4394.3 1140.1 1432.9 1031.2

It is found that the resulting volumes obtained from the new equation are much closer to the MRI data, which is believed to be the truth. However, more noise is found in a larger volume by the new method. The reason is that as the volume increases, the exponential term of the new equation would amplify the noise more rapidly than the linear Baan's equation.

The following applications are based on the above explanation.

The present invention pertains to an apparatus 500 for determining heart transplant rejection of a heart in a patient, as shown in FIGS. 11-15. The apparatus 500 comprises at least two electrodes 502 adapted to be sewn into the heart that span the left ventricle. The apparatus 500 comprises a voltage generator 504 adapted to be inserted in the patient which generates a voltage to the two electrodes 502 and senses the resulting voltage from the two electrodes 502.

Preferably, the apparatus 500 includes a third electrode 506 and a fourth electrode 508 adapted to be implanted in the LV myocardium, and wherein the voltage generator 504 determines both the magnitude and phase angle of the resulting voltage from the two electrodes 502 and the third and fourth electrodes. The voltage generator 504 is preferably adapted to be implanted in the chest of the patient and is in communication with the two electrodes 502 and the third and fourth electrodes.

The present invention pertains to a method for determining heart transplant rejection of a heart in a patient. The method comprises the steps of sewing into the heart at least two electrodes that span the left ventricle. There is the step of inserting in the patient a voltage generator which generates a voltage to the two electrodes and senses the resulting voltage from the two electrodes.

The present invention pertains to a pacemaker 600 for a patient, as shown in FIG. 18. The pacemaker will include traditional pacemakers for slow heart rates, bi-ventricular pacemakers to improve LV and RV synchrony for heart failure patients, and AICD devices with both pacing and defibrillation functions. The pacemaker 600 comprises an RV lead 602 having four electrodes 604 that span the length of the RV adapted to be inserted at the RV apex with at least one of the four electrodes placed in either the right atrium or veins drawing into the right heart of the patient. The pacemaker 602 comprises a voltage generator 606 which generates a voltage signal to the electrodes 604 and senses the instantaneous voltage in the RV and determines the real and imaginary components to remove the myocardial component from the septum and RV free wall to determine absolute RV blood volume. The pacemaker 600 comprises a battery 608 connected to the voltage generator 606. The pacemaker 600 comprises a defibrillator 610 connected to the battery 608.

Preferably, the pacemaker 600 includes a surface epicardial catheter 612 having four electrodes 614.

The present invention pertains to a method for assisting a heart of a patient. The method comprises the steps of inserting into the RV apex an RV lead of a pacemaker having four electrodes that span the length of the RV. There is the step of generating a voltage signal to the electrodes from a voltage generator. There is the step of sensing the instantaneous voltage in the RV with the voltage generator to determine the real and imaginary components of the voltage to remove the myocardial component from the septum and RV free wall to determine absolute RV blood volume.

More specifically, in regard to a non-invasive method and apparatus to determine heart transplantation rejection, patients undergoing heart transplantation continue to be routinely referred for invasive myocardial biopsy for histologic examination to determine if rejection is occurring to guide dose adjustment of immunosuppressive medications. This invasive method subjects patients to morbidity and random sampling errors. Previous noninvasive methods 11-14 have been studied and have been unsuccessful. Electrical Admittance of myocardial tissue can be used to identify transplant rejection 15. The presence of infiltrating lymphocytes, membrane injury and edema decreases electrical Admittance in the myocardium. An important contributor to the myocardial Admittance is myocyte membrane capacitance. As myocytes are damaged by the process of rejection, the capacitance will be reduced. A device attached to the healthy heart as it is transplanted, which will be monitored for rejection by telemetry can reveal the rejection process, as shown in FIGS. 11-15.

At the time of heart transplantation, the healthy heart that will be placed into the chest of the patient will have 2 to 4 electrodes sewn into the heart that span the left ventricle. These electrodes will be attached to a device that can be inserted within the chest cavity that will generate a voltage to two of these electrodes, then sense the resulting voltage with either the identical two electrodes, or electrodes 3 and 4 implanted in the LV myocardium and determine both the magnitude and phase angle of this returning signal. This device will have the capability to generate these myocardial measurements by telemetry to either a doctor's office or hospital. If the baseline resistivity of the myocardium is changing, especially the phase angle, then it will be interpreted to mean that myocardial rejection of the new heart is occurring. The patient's doctor will use this information to determine if the patient's dose of anti-rejection medications such as steroids need to be increased. Alternatively, if the resistivity of the heart returns to a safe range, then increased anti-rejection medications can be reduced. FIGS. 11-15 show two embodiments regarding this technique. In one embodiment, as shown in FIG. 12, a penetrating transducer 512 having the electrodes is inserted into the heart. In a second embodiment, a surface transducer 514 is sewn to the surface of the heart. FIG. 15 shows the various embodiments in application. Only one embodiment would be used at a time. FIGS. 16 and 17 show different placements regarding the apparatus 500.

FIG. 11 shows the penetrating transducer that is inserted into the transplanted heart. The electrodes would be disposed inside the heart with the stopper contacting the heart surface and preventing the penetrating transducer from extending further into the heart.

FIGS. 12 and 13 show a bottom view and a side view, respectively, of the surface transducer that would be attached to the surface of the transplanted heart. The electrodes are found on the surface transducer.

FIG. 14 shows the electric field lines about either the penetrating transducer or the surface transducer. It should be noted that while the penetrating transducer and the surface transducer are both shown together with the transplanted heart in FIG. 14, in reality, only one of the embodiments would be used. The presence of both transducers is simply for exemplary purposes. Similarly, FIG. 15 shows the surface transducer attached to the epicardium, or the penetrating catheter inserted either endocardially or epicardially. In practice, only one transducer would actually be used.

Variations of this device can include a hand held device that is applied to the closed chest wall, to activate the electrodes in the chest to save on battery usage. The device in the chest can also utilize the motion of the heart to self generate energy as well, by translating the torsional motion of the heart into electric energy.

Another application, as shown in FIG. 18, is the determination of RV volume coupled to a pacemaker/defibrillator lead 602 in the RV. AICD are now recommended in any heart failure patient with an LVEF of less than 30%. There is also an effort to reduce hospital admissions for patients due to episodes of CHF by detecting right heart pressures to alert the patient that they are going into fluid overload before the clinical entity of CHF occurs. Since the right and left ventricular pressure-volume relations during filling (diastole) are relatively flat, there is a large change in volume for a small change in pressure. Hence, detecting RV volume accurately will be a more sensitive marker of the development of impending CHF than will be RV or pulmonary artery pressure, or trans-lung impedance the latter an indirect measure of pulmonary edema. Thus, the placement of 4 electrodes on the RV lead that span the length of the RV of a AICD/pacemaker to be implanted in a patient with a reduced LVEF coupled with phase angle (the function generator board placed in the battery-circuit of the device) to provide instantaneous RV volume via telemetry can be used to generate the gold standard for impending heart failure, instantaneous RV volume.

The AICD lead 602 that is in the right ventricle and inserted into the RV apex has 2 to 4 electrodes 604 mounted on it. The AICD battery 608 that is already implanted under the skin can also be used to then generate a voltage signal between electrodes 1 and 4 on the RV lead 602, and sense the instantaneous voltage in the RV and determine the real and imaginary components to remove the myocardial component of the septum and RV free wall to determine absolute RV blood volume. The additional electronic circuits for phase angle can be added to the device already implanted under the skin as well.

The patient at home can via telemetry send to their doctor the phase angle information from the RV chamber, and determine if the RV volume is increasing or not. If it has increased, before the patient has had symptoms of congestive heart failure, then the patient's medications can be altered to remove fluid (diuresis) in order to avoid future hospitalization.

RV volume will be more sensitive that telemetric RV pressure since as the RV dilates, it maintains a similar pressure. It will also be in competition with a device made by Medtronic, Inc., which determines the impedance of the entire chest as an indirect method to determine if the lungs are filling with fluid (pulmonary edema) before the patient needs to be hospitalized with congestive heart failure. The Medtronic device is limited because it is determining impedance not only of the lungs, but the entire chest wall.

Although the invention has been described in detail in the foregoing embodiments for the purpose of illustration, it is to be understood that such detail is solely for that purpose and that variations can be made therein by those skilled in the art without departing from the spirit and scope of the invention except as it may be described by the following claims.

APPENDIX

The following is a list of references, identified herein, all of which are incorporated by reference herein.

-   1. Baan, J., Jong, T., Kerkhof, P., Moene, R., van Dijk, A., van der     Velde, E., and Koops, J.; Continuous stroke volume and cardiac     output from intra-ventricular dimensions obtained with impedance     catheter. Cardiovascular Research, v15, pp 328-334, 1981. -   2. J. Baan, E. van der Velde, H. deBruin, G. Smeenk, J. Koops, A.     vanDijk, D. Temmerman, J. Senden, and B. Buis; Continuous     measurement of left ventricular volume in animals and humans by     conductance catheter. Circulation, v70, n5, pp 812-823, 1984. -   3. Burkhoff D., Van der Velde E., Kass a, Baan J., Maughan W L.,     Sagawa K.; Accuracy of volume measurement by conductance catheter in     isolated, ejecting canine hearts. Circulation 72:440-447, 1985. -   4. MacGowan G A, Haber H L, Cowart T D, Tedesco C, Wu C C, Feldman M     D; Direct myocardial effects of OPC-18790 in human heart failure:     beneficial effects on contractile and diastolicfunction demonstrated     by intracoronary infusion with pressure-volume analysis. JACC     31:1344-1351, 1998. -   5. Steendijk, P., Mur, G., Van der Velde, E. and Baan, J.; The     four-electrode resistivity technique in anisotropic media:     theoretical analysis and application in myocardial tissue in vivo.     IEEE Trans. on Biomed. Engr., v40, n11, pp 1138-1148, 1993. -   6. Sperelakis, N. and Hoshiko, T.; Electrical impedance of cardiac     muscle. Circ. Res. v9, pp 1280-1283, 1961. -   7. Richard D. Stay, Kenneth R. Foster, Herman P. Schwan; Dielectric     properties of mammalian tissues from 0.1 to 100 MHz: a summary of     recent data. Physics in Medicine and Biology, v27, n4, pp 501-513,     1982. -   8. Steendijk, P., Mur, G., Van der Velde, E. and Baan, J.; The     four-electrode resistivity technique in anisotropic media:     theoretical analysis and application in myocardial tissue in vivo.     IEEE Trans, on Biomed. Engr., v40, n11, pp 1138-1148, 1993. -   9. Steendijk, P., Mur, G., Van der Velde, E. and Baan, J.;     Dependence of anisotropic myocardium electrical resistivity on     cardiac phase and excitation frequency. Basic Res. Cardiol., v89, pp     411-426, 1994. -   10. Gabriel, C., Gabriel, S., Corthout E.; The dielectric properties     of biological tissues: I. Literature survey. Physics in Medicine and     Biology, v41, n11, pp 2231-2249, 1996. -   11. Gabriel, S., Lau, R W, Gabriel, C.; The dielectric properties of     biological tissues: II. Measurements in the frequency range 10 Hz to     20 GHz. Physics in Medicine and Biology, v41, n11, pp 2251-2269,     1996. -   12. Gabriel, S., Lau, R W, Gabriel, C.; The dielectric properties of     biological tissues: III. Parametric models for the dielectric     spectrum of tissue. Physics in Medicine and Biology, v41, n11, pp     2271-2293, 1996. -   13. Tsai, J-Z, Will, J. A., Hubard-van Stelle, S., Cao, H., Tungj     itkusolmun, S., Choy, Y. B., Haemmerich, D., Vorperian, V. R., and     Webster, J. G.; In-vivo measurement of swine myocardial resistivity.     IEEE Trans. Biomed. Engr., v49, n5, pp 472-483, 2002. -   14. Tsai, J-Z, Will, J. A., Hubard-van Stelle, S., Cao, H.,     Tungjitkusolmun, S., Choy, Y. B., Haemmerieh, D., Vorperian, V. R.,     and Webster, J. G.; Error analysis of tissue resistivity     measurement. IEEE Trans. Biomed. Engr., v49, n5, pp 484-494, 2002. 

What is claimed is:
 1. An implantable pacemaker for a patient comprising: a right ventricular (RV) lead having a plurality of electrodes spanning a length of the RV adapted to be inserted into an RV apex; a voltage generator configured to generate a voltage signal to the electrodes and sense an instantaneous voltage in the RV and determine real and imaginary components to remove a myocardial component of a septum and RV free wall to determine absolute RV blood volume; a battery connected to the voltage generator; a defibrillator connected to the battery; and a bi-ventricular pacemaker configured to resynchronize RV and left ventricle (LV) ventricular contraction based on the absolute blood volume to avoid heart failure.
 2. The pacemaker as described in claim 1 including a voltage regulator having a processor.
 3. The pacemaker as described in claim 2 including a pressure sensor configured for measuring instantaneous pressure of a heart chamber in communication with the processor.
 4. The pacemaker as described in claim 3 wherein the processor is configured to produce a single waveform at a desired frequency for the RV lead.
 5. The pacemaker as described in claim 3 wherein the processor is configured to produce a plurality of desired waveforms at single or multiple desired frequencies for the RV lead.
 6. The pacemaker as described in claim 5 wherein the processor is configured to produce the plurality of desired waveforms at single or multiple desired frequencies simultaneously, and the processor is configured to separate the plurality of desired wave forms at desired frequencies the processor receives from the RV lead.
 7. The pacemaker as described in claim 6 wherein the plurality of electrodes are configured to measure a least one segmental volume of a heart chamber.
 8. The pacemaker as described in claim 7 wherein the absolute RV blood volume is determined according to a non-linear relationship is β(G)(σ=0.928S/m)=1+1.774(10^(7.481×10) ⁻⁴ ^((G−2057))) where: G is the measured conductance (S), the calculations have been corrected to the conductivity of whole blood at body temperature (0.928 S/m), and 2057 is the asymptotic conductance in μS when a cuvette is filled with a large volume of whole blood.
 9. The pacemaker as described in claim 8 wherein blood volume with respect to time as measured by the electrodes of the RV lead is determined according to ${{Vol}(t)} = {{\left\lbrack {\beta (G)} \right\rbrack \left\lbrack \frac{L^{2}}{\sigma_{b}} \right\rbrack}\left\lbrack {{Y(t)} - Y_{p}} \right\rbrack}$ where: β(G)=the field geometry calibration function (dimensionless), Y(t)=the measured combined admittance, σ_(b) is blood conductivity, L is distance between measuring electrodes, and Y_(p)=the parallel leakage admittance, dominated by cardiac muscle.
 10. The pacemaker as described in claim 9 wherein the pressure sensor is in contact with the RV lead to measure ventricular pressure in the RV.
 11. The pacemaker as described in claim 10 wherein the plurality of electrodes includes intermediate electrodes configured to measure an instantaneous voltage signal from the heart, and outer electrodes to which a current is applied from the processor.
 12. The pacemaker as described in claim 11 wherein the pressure sensor is disposed between the intermediate electrodes and the outer electrodes.
 13. The pacemaker as described in claim 12 wherein the computer is configured to convert conductance into a volume.
 14. The pacemaker as described in claim 7 wherein blood volume with respect to time as measured by the electrodes of the RV lead is determined according to Vol(t)=ρL ² g _(b)(t)exp[γ·(g _(b)(t))²] where Vol(t) is the instantaneous volume, ρ is the blood resistivity, L is the distance between the sensing electrodes, g_(b)(t) is the instantaneous blood conductance, and γ is an empirical calibration factor.
 15. A method for assisting a heart of a patient comprising the steps of: inserting into a right ventricle (RV) apex an RV lead of a pacemaker having a plurality of electrodes that span a length of the RV; generating a voltage signal to the electrodes from a voltage generator; and sensing an instantaneous voltage in the RV with the voltage generator to determine real and imaginary components of the voltage to remove a myocardial component of the septum and RV free wall to determine absolute RV blood volume based on the absolute blood volume to avoid heart failure.
 16. A method as described in claim 15 including the step of producing a plurality of desired wave forms at desired frequencies for the RV lead.
 17. A method as described in claim 16 wherein the producing step includes the step of producing the plurality of desired waveforms at desired frequencies simultaneously, and including the step of a processor separating the plurality of desired waveforms at desired frequencies the processor received from the RV lead.
 18. A method as described in claim 17 wherein the sensing step includes the step of the voltage generator applying a non-linear relationship according to β(G)(σ=0.928S/m)=1+1.774(10^(7.481×10) ⁻⁴ ^((G−2057))) where: G is the measured conductance (S), the calculations have been corrected to the conductivity of whole blood at body temperature (0.928 S/m), and 2057 is the asymptotic conductance in μS when a cuvette is filled with a large volume of whole blood.
 19. A method as described in claim 18 wherein the sensing step includes the step of determining instantaneous volume according to ${{Vol}(t)} = {{\left\lbrack {\beta (G)} \right\rbrack \left\lbrack \frac{L^{2}}{\sigma_{b}} \right\rbrack}\left\lbrack {{Y(t)} - Y_{p}} \right\rbrack}$ where: β(G)=the field geometry calibration function (dimensionless), Y(t)=the measured combined admittance, and Y_(p)=the parallel leakage admittance, dominated by cardiac muscle.
 20. The method of claim 19 including the step of treating the patient if the RV volume is increasing. 